Talk:Berezinskii–Kosterlitz–Thouless transition

Any chance to mention V.L. Berezinskii (who showed the existence of phase transition and demonstrated the role of vortices)?

I just did an ambiguation page for Thouless. How about something that tells us what field this is? maybe "...interacting spin systems in theoretical physics of the electron". (That's wrong no doubt, but you get my drift? Thanks --Singkong2005 03:08, 20 December 2005 (UTC)

hardly understandable
I am experimentalist working in superconductivity, but for me it is hard to understand this explanation (language).

For example, "...This is because the expected ordered phase of the system is destroyed by transverse fluctuations".....what transverse fluctuations?

Further "the Goldstone modes (see Goldstone boson) associated with this broken continuous symmetry". Which "this" symmetry?

In analysis, what is $$S^1$$? What is "universal cover R"?

Then, the positions of the vortices are denoted by $$x_i$$, then they become $$z_i$$??? Can it be explained how this transition is done? I assume that real and imaginary axes are just x and y axes in our 2D problem.

It is written "it is easy to see that the second term is positive infinite". For me it is not so easy to see, although I can guess that gradient is constant all over, so it integrates to infinity. But what about "branch cuts"? do we ignore them or what?

How the expression with logarithm was obtained?

The phrase "This is nothing other than a Coulomb gas". What this? The sum above?

In the last paragraph I found a hint that vortices can actually move as a result of fluctuations or something? So, what are the assumptions? Can they be fully formulated?

In summery, the present version can be understood only by specialists and very mathematical. It does not look like a an enciclopedia article which can be read and understood by a student studying e.g. atomic physics.

Edward 21:45, 25 November 2006 (UTC)

Hi Edward. I'm inclined to agree. We could put in a section that describes the reasons for it more physically. For example: ``A single flux line passing directly through a cube with side length l has free energy of el, where e is the free energy per unit length. However this ignores the entropy from the number of ways of arranging the line, which is of order l^2/s^2, where s is the spacing between flux-line sites. The corresponding entropy is therefore 2k\ln(l/s), and the total free energy will be of order el-2kT\ln(l/s). Clearly the first term dominates, and so the entropy of the arrangements may be ignored. In a thin film or two dimensional system, however, the situation changes. Now the free energy is f (which is independent of l), and the total free energy for one flux line becomes f-2kT(l/s). This is negative when T>f/2k\ln(l/s), and the film then spontaneously fills with vortex-antivortex pairs, and loses phase coherence and its superfluid properties. This is the KT transition." Source is "Superconductivity of Metals and Cuprates" by J. R. Waldram.

Although this example is not entirely general, I think, I believe it helps make clear what's happening. Grj23 (talk) 05:24, 30 September 2009 (UTC)


 * Goldstone bosons and symmetry breaking are cool, but I shouldn't have to look at the citations to make sure I'm not editing a math page. The justification for the KT transition using thermodynamics is a good start, but maybe we should include something in the intro that actually says plainly what it is and what systems we see it in.(Example: Josephson Junction arrays.)Duergan (talk) 06:19, 22 August 2011 (UTC)

Vortex-Antivortex Pairs
It's odd to see an article on the KT transition that doesn't include vortex anti-vortex pairs, as most of the experimental papers I've seen are concerned with KT transition from lower energy bound pairs to higher energy dissociated pairs. — Preceding unsigned comment added by Duergan (talk • contribs) 16:47, 22 August 2011 (UTC)

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variable z
It's not clear what $$z_i$$ (some complex value at the defect location) $$z$$ (value of some complex quantity ... everywhere else?) are. Perhaps $$\phi$$ is meant? A similar formulation is not used in any of the sources. CyreJ (talk) 06:54, 15 August 2020 (UTC)